What are the implications of "le'Achas me'Eileh"?
Shevu'os, 28b: It implies that one is only Chayav one Korban and not two
What if he swears that he will not eat and he subsequently eats many different foods of eats and drinks?
Sifra: We learn from "Ashamo ... al Chataso ... " (in Pasuk 6 - all in the singular) that he is only Chayav one Korban.
What are the connotations of "ve'Hisvadah"?
Rashi (in Shevu'os) and Ramban (citing Sifri Zuta): It teaches us that all Chata'os (and Ashamos
Why does the Torah mention Viduy specifically here, and not by any of the other Chata'os?
Ramban #1 and Moshav Zekenim #1: Because, Shevu'as ha'Eidus, unlike the Chata'os mentioned earlier in the Parshah, is Chayav even be'Meizid. 1
Ramban #2 (citing the Sifri Zuta) and Moshav Zekenim #2: The Mitzvah of Viduy actually applies to all the Chata'os mentioned in the Parshah, and the Torah mentions it here because Shevu'as ha'Eidus and Shevu'as Bituy (in Pasuk 4) are not subject to Kareis. How much more so is Viduy is needed for Chayvei Kerisus!